You and a friend pass by a standard coin operated vending machine and you decide to get a candy bar.
The price is US $0.95, but after checking your pockets you only have a dollar (US $1) and the machine
only takes coins. You turn to your friend and have this conversation:
you: Hey, do you have change for a dollar?
friend: Let's see. I have 6 US coins but, although they add up to a US $1.15, I can't break a dollar.
you: Huh? Can you make change for half a dollar?
friend: No.
you: How about a quarter?
friend: Nope, and before you ask I cant make change for a dime or nickel either.
you: Really? and these six coins are all US government coins currently in production?
friend: Yes.
you: Well can you just put your coins into the vending machine and buy me a candy bar, and I'll pay you back?
friend: Sorry, I would like to but I cant with the coins I have.
What coins are your friend holding?

To be fair, the problem has no solution mathematically. But there is a solution when one takes into account that
vending machines typically do not take the 50 cent coins!